Skip to content

komm.UniformQuantizer

Uniform scalar quantizer. It is a scalar quantizer in which the separation between levels is constant, $\Delta$, and the thresholds are the mid-point between adjacent levels. For more details, see Say06, Sec. 9.4.

Attributes:

  • num_levels (int) –

    The number of quantization levels $L$. It must be greater than $1$.

  • input_range (tuple[float, float]) –

    The range $(x_\mathrm{min}, x_\mathrm{max})$ of the input signal. Default is $(-1.0, 1.0)$.

  • choice (Literal['mid-riser', 'mid-tread']) –

    The choice for the uniform quantizer. Must be either 'mid-riser' or 'mid-tread'. Default is 'mid-riser'.

Examples:

>>> quantizer = komm.UniformQuantizer(
...     num_levels=4,
...     input_range=(-1.0, 1.0),
...     choice='mid-riser',
... )
>>> quantizer.levels
array([-0.75, -0.25,  0.25,  0.75])
>>> quantizer.thresholds
array([-0.5,  0. ,  0.5])

>>> quantizer = komm.UniformQuantizer(
...     num_levels=4,
...     input_range=(-1.0, 1.0),
...     choice='mid-tread',
... )
>>> quantizer.levels
array([-1. , -0.5,  0. ,  0.5])
>>> quantizer.thresholds
array([-0.75, -0.25,  0.25])

>>> quantizer = komm.UniformQuantizer(
...     num_levels=4,
...     input_range=(0.0, 1.0),
...     choice='mid-tread',
... )
>>> quantizer.levels
array([0.  , 0.25, 0.5 , 0.75])
>>> quantizer.thresholds
array([0.125, 0.375, 0.625])

quantization_step float cached property

The quantization step $\Delta$.

Examples:

>>> quantizer = komm.UniformQuantizer(num_levels=4, input_range=(-4, 4))
>>> quantizer.quantization_step
2.0

levels NDArray[floating] cached property

The quantizer levels $v_0, v_1, \ldots, v_{L-1}$.

Examples:

>>> quantizer = komm.UniformQuantizer(num_levels=4, input_range=(-4, 4))
>>> quantizer.levels
array([-3., -1.,  1.,  3.])

thresholds NDArray[floating] cached property

The quantizer finite thresholds $t_1, t_2, \ldots, t_{L-1}$.

Examples:

>>> quantizer = komm.UniformQuantizer(num_levels=4, input_range=(-4, 4))
>>> quantizer.thresholds
array([-2.,  0.,  2.])

mean_squared_error()

Computes the mean squared (quantization) error (MSE) of the quantizer for a given input probability density function (pdf). It is defined as $$ \mse = \int_{-\infty}^{\infty} (x - y)^2 f_X(x) \, dx $$ where $y$ is the quantized signal and $f_X(x)$ is the pdf of the input signal.

Parameters:

  • input_pdf (Callable[[NDArray[floating]], NDArray[floating]]) –

    The probability density function $f_X(x)$ of the input signal.

  • input_range (tuple[float, float]) –

    The range $(x_\mathrm{min}, x_\mathrm{max})$ of the input signal.

  • points_per_interval (int) –

    The number of points per interval for numerical integration (default: 4096).

Returns:

  • mse (float) –

    The mean square quantization error.

Examples:

>>> quantizer = komm.UniformQuantizer(num_levels=4, input_range=(-4, 4))
>>> gaussian_pdf = lambda x: 1/np.sqrt(2*np.pi) * np.exp(-x**2/2)
>>> quantizer.mean_squared_error(
...     input_pdf=gaussian_pdf,
...     input_range=(-5, 5),
... )
0.3363025489037716
>>> uniform_pdf = lambda x: 1/8 * (np.abs(x) <= 4)
>>> quantizer.mean_squared_error(
...     input_pdf=uniform_pdf,
...     input_range=(-4, 4),
... )
0.3333333730891729
>>> quantizer.quantization_step**2 / 12
0.3333333333333333

digitize()

Returns the quantization indices for the input signal.

Parameters:

  • input (ArrayLike) –

    The input signal $x$ to be digitized.

Returns:

  • output (NDArray[integer]) –

    The integer indices of the quantization levels for each input sample.

Examples:

>>> quantizer = komm.UniformQuantizer(num_levels=4, input_range=(-4, 4))
>>> quantizer.digitize([-2.4,  0.8,  3.2])
array([0, 2, 3])

quantize()

Quantizes the input signal.

Parameters:

  • input (ArrayLike) –

    The input signal $x$ to be quantized.

Returns:

  • output (NDArray[floating]) –

    The quantized signal $y$.

Examples:

>>> quantizer = komm.UniformQuantizer(num_levels=4, input_range=(-4, 4))
>>> quantizer.quantize([-2.4,  0.8,  3.2])
array([-3.,  1.,  3.])